Early work on deformable object manipulation uses predefined visual features for object state estimation [1]}, [2]} and plans with handcrafted approximate dynamics models, e.g., linear models [3]}, [4]}, [5]}, [6]}.
One major difficulty is a powerful representation that connects rich visual perception and complex object dynamics for long-horizon robot manipulation planning.
The recent advances in data-driven methods, especially, deep learning, have brought up significant interests in learning model-free policies [7]}, [8]}, [9]}, [10]}, [11]} or dynamics models  [12]}, [13]}, [14]} from raw visual images. However, a lot of prior works on model learning use the unstructured state representation as a single vector (see, e.g.,  [15]}, [16]}).
Structured representations, such as particles [17]}, [18]} or graphs [19]}, [17]}, [21]}, [22]}, [23]}, generally improve the predictive power and generalization capability of the learned models. Hence, G-DOOM uses a learned graph by GNNs to represent the object's dynamic state.
